UID:
almahu_9947367688602882
Format:
1 online resource (357 p.)
Edition:
1st ed.
ISBN:
1-281-27957-9
,
9786611279578
,
0-08-053785-5
Series Statement:
Studies in mathematics and its applications, v. 32
Content:
Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and func
Note:
Description based upon print version of record.
,
Cover; Contents; Introduction; Notations; Chapter 1. Basic examples; 1.1 Introduction; 1.2 The Haar system; 1.3 The Schauder hierarchical basis; 1.4 Multivariate constructions; 1.5 Adaptive approximation; 1.6 Multilevel preconditioning; 1.7 Conclusions; 1.8 Historical notes; Chapter 2. Multiresolution approximation; 2.1 Introduction; 2.2 Multiresolution analysis; 2.3 Refinable functions; 2.4 Subdivision schemes; 2.5 Computing with refinable functions; 2.6 Wavelets and multiscale algorithms; 2.7 Smoothness analysis; 2.8 Polynomial exactness; 2.9 Duality, orthonormality and interpolation
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2.10 Interpolatory and orthonormal wavelets2.11 Wavelets and splines; 2.12 Bounded domains and boundary conditions; 2.13 Point values, cell averages, finite elements; 2.14 Conclusions; 2.15 Historical notes; Chapter 3. Approximation and smoothness; 3.1 Introduction; 3.2 Function spaces; 3.3 Direct estimates; 3.4 Inverse estimates; 3.5 Interpolation and approximation spaces; 3.6 Characterization of smoothness classes; 3.7 LP-unstable approximation and 0 〈 p 〈 1; 3.8 Negative smoothness and LP-spaces; 3.9 Bounded domains; 3.10 Boundary conditions; 3.11 Multilevel preconditioning
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3.12 Conclusions3.13 Historical notes; Chapter 4. Adaptivity; 4.1 Introduction; 4.2 Nonlinear approximation in Besov spaces; 4.3 Nonlinear wavelet approximation in Lp; 4.4 Adaptive finite element approximation; 4.5 Other types of nonlinear approximations; 4.6 Adaptive approximation of operators; 4.7 Nonlinear approximation and PDE's; 4.8 Adaptive multiscale processing; 4.9 Adaptive space refinement; 4.10 Conclusions; 4.11 Historical notes; References; Index
,
English
Additional Edition:
ISBN 1-4933-0227-2
Additional Edition:
ISBN 0-444-51124-5
Language:
English
